Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 9$ and $ JT = 4x + 3$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 9} = {4x + 3}$ Solve for $x$ $ 3x = 12$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({4}) - 9$ $ JT = 4({4}) + 3$ $ CJ = 28 - 9$ $ JT = 16 + 3$ $ CJ = 19$ $ JT = 19$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {19} + {19}$ $ CT = 38$